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Applications of Hypergroups and Related Measure Algebras
Edited by: William C. Connett, Marc-Olivier Gebuhrer, and Alan L. Schwartz

Contemporary Mathematics
1995; 441 pp; softcover
Volume: 183
ISBN-10: 0-8218-0297-6
ISBN-13: 978-0-8218-0297-7
List Price: US$84
Member Price: US$67.20
Order Code: CONM/183
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"The most important single thing about this conference was that it brought together for the first time representatives of all major groups of users of hypergroups. [They] talked to each other about how they were using hypergroups in fields as diverse as special functions, probability theory, representation theory, measure algebras, Hopf algebras, and Hecke algebras. This led to fireworks."--from the Introduction

Hypergroups occur in a wide variety of contexts, and mathematicians the world over have been discovering this same mathematical structure hidden in very different applications. The diverse viewpoints on the subject have led to the need for a common perspective, if not a common theory. Presenting the proceedings of a Joint Summer Research Conference held in Seattle in the summer of 1993, this book will serve as a valuable starting point and reference tool for the wide range of users of hypergroups and make it easier for an even larger audience to use these structures in their work.


Advanced graduate students and researchers in measure algebras, statisticians and physicists.

Table of Contents

  • N. B. Salem and M. N. Lazhari -- Limit theorems for some hypergroup structures on \({\mathbb R}^n\times [0,\infty [\)
  • Yu. M. Berezansky -- Nuclear spaces of test functions connected with hypercomplex systems and representations of such systems
  • Yu. M. Berezansky and A. A. Kalyuzhnyi -- Hypercomplex systems and hypergroups: Connections and distinctions
  • W. R. Bloom and Z. Xu -- The Hardy-Littlewood maximal function for Chébli-Trimèche hypergroups
  • H. Chebli -- Sturm-Liouville hypergroups
  • W. C. Connett and A. L. Schwartz -- Continuous \(2\)-variable polynomial hypergroups
  • P. Eymard -- A survey of Fourier algebras
  • A. Fitouhi and M. M. Hamza -- Expansion in series of Laguerre functions for solution of perturbed Laguerre equations
  • L. Gallardo -- Asymptotic behaviour of the paths of random walks on some commutative hypergroups
  • M.-O. Gebuhrer -- Bounded measures algebras: A fixed point approach
  • H. Heyer -- Progress in the theory of probability on hypergroups
  • T. H. Koornwinder -- Discrete hypergroups associated with compact quantum Gelfand pairs
  • B. M. Levitan -- Transmutation operators and the inverse spectral problem
  • M. Mabrouki -- Limit theorems for the spin process
  • N. H. Mahmoud -- Differential operators with matrix coefficients and transmutations
  • B. P. Osilenker -- Generalized product formulas for orthogonal polynomials
  • G. B. Podkolzin -- An infinitesimal algebra of the hypergroup generated by double cosets and nonlinear differential equations
  • M. Rösler -- Convolution algebras which are not necessarily positivity-preserving
  • K. A. Ross -- Signed hypergroups--A survey
  • V. S. Sunder -- On the relation between subfactors and hypergroups
  • R. Szwarc -- Connection coefficients of orthogonal polynomials with applications to classical orthogonal polynomials
  • K. Trimeche -- Generalized transmutation and translation operators associated with partial differential operators
  • L. Vainerman -- Gel'fand pairs of quantum groups, hypergroups and \(q\)-special functions
  • M. Voit -- Central limit theorems for Jacobi hypergroups
  • N. J. Wildberger -- Finite commutative hypergroups and applications from group theory to conformal field theory
  • H. Zeuner -- Kolmogorov's three series theorem on one-dimensional hypergroups
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